# On the Exchange Interactions in Holographic p-adic CFT

## TL;DR

This paper analyzes exchange interactions in p-adic conformal field theories using holographic Witten diagrams, providing a complete calculation of four-point correlators and discussing their singularity structure.

## Contribution

It offers the first detailed computation of exchange contributions to four-point functions in holographic p-adic CFTs, including contact terms and Mellin space analysis.

## Key findings

- Exchange interactions significantly affect four-point correlators.
- The models are analogous to AdS2/CFT1.
- Complete correlator expressions are derived.

## Abstract

There is a renewed interest in conformal field theories (CFT) on ultrametric spaces (p-adic field and its algebraic extensions) in view of their natural adaptability in the holographic setting. We compute the contributions from the exchange interactions to the four-point correlator of the CFT using Witten diagrams with three-scalar interaction vertex. Together with the contributions from the bulk four-point interaction, the contact term, these provide a complete answer. We remark on the singularity structure in Mellin space, and argue that all these models are analogues of adS_2/CFT_1.